Generalized scaling laws for the formation of plasma confining potentials are investigated to find the physics essentials common to representative tandem-mirror operational modes in GAMMA 10. These modes are characterized in terms of (i) a high-potential mode and (ii) a hot-ion mode. The potential-formation scalings in these modes are consolidated and generalized on the basis of the consistency with finding of the wider validity of Cohen's strong electron-cyclotron heating (ECH) theory covering over both modes. A plateau-shaped electron distribution function is observed when a plug electron-confining potential is formed in the hot ion mode of GAMMA 10, as predicted in terms of the strong ECH theory.